Any apparatus can be assigned a local three-dimensional coordinate system. For example, a rectangular brick can be assigned a local Cartesian coordinate system that describes its length, width and height relative to a specific corner of the brick. The rotational orientation of the apparatus' local coordinate system with respect to a geographical coordinate system is defined by a quaternion. The quaternion gives the direction of the rotation axis and the magnitude of the rotation.
This apparatus is used to determine this rotation quaternion. The apparatus requires that three conditions be satisfied: (1) a gravitational field must be present (2) the apparatus must be non-moving in the geographical coordinate system, and (3) the geographical coordinate system must be a non-inertial rotating coordinate system. An example satisfying all conditions would be determining the orientation of an apparatus placed stationary on or beneath the Earth's surface.
Applications for this apparatus include determining the orientation of instruments placed on the ocean floor by remotely-operated vehicles and determining the inclination and azimuth of instruments placed in boreholes that are drilled into the Earth's surface. Borehole inclinometers have applications in the mining, geotechnical, and petroleum industries to determine the trajectory of boreholes in the ground. They are also used to determine the orientation of various subsurface mechanisms such as directional drilling motors, kick-off wedges, and core orientation systems. Typically, such an instrument is moved through the borehole with centralizing mechanisms to keep its long axis aligned with the borehole; measurements of borehole orientation are made at depth intervals and then an interpolation scheme, of which many exist as prior art, is used to compute a trajectory for the borehole.
To compute the rotation quaternion, the apparatus must make measurements of two independent geographical reference vectors. Such vectors have a known magnitude and direction for any given location on the Earth's surface. The three available reference vectors are gravity, the Earth's magnetic field, and the Earth's axial spin.
Measuring the gravitational acceleration vector is straightforward using one or more accelerometers, and is prior art. Measuring the Earth's magnetic field is also straightforward using one or more magnetic sensors having directional sensitivity. A problem with using the magnetic field arises when the Earth's magnetic field is distorted by the presence of nearby magnetic material (e.g., magnetic rock or steel structures). These disturbances introduce errors in the computed apparatus orientation. Undisturbed measurements of the Earth's magnetic field together with measurements of the acceleration vector to determine relative orientation is prior art.
Measuring the Earth's rotation vector is not straightforward and is the subject of many patents. The signal is reliable, but small. The maximum signal strength is 15°/hour, or approximately 0.004°/s—an angular rate sensor must be able to resolve a small fraction of this maximum value in order to be useful. Historically, sensors capable of directly measuring the Earth rotation signal have been expensive, and some are sensitive to mechanical shock or vibration. In recent years, the development of FOG (fibre-optic gyros) and MEMS (micro-electrical machined structure) angular rate sensors has brought the promise of inexpensive, rugged sensors capable of measuring Earth rotation. Unfortunately, some of these sensors exhibit sensitivity to linear acceleration (e.g., gravity) so that for small signals, it may be difficult to discriminate between linear acceleration and angular rotation.
The use of accelerometers to measure the direction and magnitude of the Earth's gravitational field in the local coordinate system is well known, as is the use of magnetometers to measure the Earth's magnetic field. U.S. Pat. No. 5,194,872 teaches reversing the sensor package to remove sensor offset bias. U.S. Pat. No. 7,813,878 uses misalignment plus rotation about the Z-axis to determine tool face orientation. Similar teachings can be found in U.S. Pat. No. 6,347,282 and U.S. Pat. No. 6,529,834. U.S. Pat. No. 7,412,775 uses a rotating table, rotating on a vertical axis, and a single MEMS gyro to determine North by looking at phase relationship. Similar teachings can be found in U.S. Pat. No. 3,753,296. U.S. Pat. No. 4,433,491, U.S. Pat. No. 3,753,296, and U.S. Pat. No. 3,894,341—rotate mechanical gyros to find maximum signal strength, on the premise that at maximum signal strength the heading must be aligned with North (Earth rotation axis). U.S. Pat. No. 5,432,699 uses orthogonal sensors and two sets of measurements separated in time and position of the apparatus to compensate for motion of the apparatus. This is a patent discussing how to correct for unwanted, but unavoidable, motion of the apparatus. U.S. Pat. Nos. 4,472,884, 4,471,533, 4,468,863, 4,559,713, 4,265,028, and 4,197,654 all use a canted gyro sensor together with rotation to permit measurement of rotation on a plurality of axes using only one sensor.